Worksheet: Equation of a Straight Line: Vector Form

In this worksheet, we will practice finding the equation of a straight line in vector form.

Q1:

Which of the following can be the vector form of the equation of the straight line π‘Žπ‘₯+𝑏𝑦+𝑐=0, where π‘Žβ‰ 0 and 𝑏≠0?

  • A r =  𝑐 π‘Ž , 0 ο‡Ά + 𝐾 ⟨ π‘Ž , βˆ’ 𝑏 ⟩
  • B r =  0 , βˆ’ 𝑐 𝑏 ο‡Ά + 𝐾 ⟨ 𝑏 , βˆ’ π‘Ž ⟩
  • C r =  0 , 𝑐 𝑏 ο‡Ά + 𝐾 ⟨ 𝑏 , βˆ’ π‘Ž ⟩
  • D r =  βˆ’ 𝑐 π‘Ž , 0 ο‡Ά + 𝐾 ⟨ π‘Ž , βˆ’ 𝑏 ⟩
  • E r =  𝑐 π‘Ž , 0 ο‡Ά + 𝐾 ⟨ π‘Ž , 𝑏 ⟩

Q2:

Which of the following can be the vector form of the equation of the straight line π‘₯π‘Ž+𝑦𝑏=1, where π‘Žβ‰ 0 and 𝑏≠0?

  • A r = ⟨ π‘Ž , 0 ⟩ + 𝐾 ⟨ π‘Ž , βˆ’ 𝑏 ⟩
  • B r = ο€Ό 0 , 1 π‘Ž  + 𝐾 ( βˆ’ 𝑏 , π‘Ž )
  • C r = ⟨ 0 , 𝑏 ⟩ + 𝐾 ⟨ π‘Ž , 𝑏 ⟩
  • D r =  0 , 1 𝑏 ο‡· + 𝐾 ⟨ 𝑏 , π‘Ž ⟩
  • E r =  βˆ’ 1 π‘Ž , 0 ο‡· + 𝐾 ⟨ 𝑏 , βˆ’ π‘Ž ⟩

Q3:

Find the vector equation of the straight line passing through the origin and the point (0,4).

  • A r = ⟨ 0 , 4 ⟩
  • B r K = ⟨ 4 , 0 ⟩
  • C r = ⟨ 4 , 0 ⟩
  • D r K = ⟨ 0 , 4 ⟩

Q4:

Find the vector equation of the straight line passing through the points (6,βˆ’7) and (βˆ’4,6).

  • A r = ⟨ βˆ’ 4 , 6 ⟩ + 𝐾 ⟨ βˆ’ 1 3 , 1 0 ⟩
  • B r = ⟨ βˆ’ 4 , 6 ⟩ + 𝐾 ⟨ 1 0 , 1 3 ⟩
  • C r = ⟨ 6 , βˆ’ 7 ⟩ + 𝐾 ⟨ 1 0 , βˆ’ 1 3 ⟩
  • D r = ⟨ 6 , βˆ’ 4 ⟩ + 𝐾 ⟨ βˆ’ 7 , 6 ⟩

Q5:

Find the vector equation of the straight line whose slope is βˆ’83 and passes through the point (4,βˆ’9).

  • A r = ⟨ 3 , βˆ’ 8 ⟩ + 𝐾 ⟨ 4 , βˆ’ 9 ⟩
  • B r = ⟨ 4 , βˆ’ 9 ⟩ + 𝐾 ⟨ 8 , βˆ’ 3 ⟩
  • C r = ⟨ βˆ’ 9 , 4 ⟩ + 𝐾 ⟨ 3 , βˆ’ 8 ⟩
  • D r = ⟨ 4 , βˆ’ 9 ⟩ + 𝐾 ⟨ 3 , βˆ’ 8 ⟩

Q6:

Consider the line through the point (3,6) and perpendicular to vector r=⟨3,6⟩. Which of the following is a vector equation of this line?

  • A 𝐾 = ⟨ 3 , 6 ⟩ + ⟨ 6 , βˆ’ 3 ⟩ r
  • B r = ⟨ 3 , 6 ⟩ + 𝐾 ⟨ 6 , βˆ’ 3 ⟩
  • C r = ⟨ 3 , 6 ⟩ + 𝐾 ⟨ 3 , 6 ⟩
  • D r = ⟨ 6 , βˆ’ 3 ⟩ + 𝐾 ⟨ 3 , 6 ⟩
  • E 𝐾 = ⟨ 3 , 6 ⟩ + ⟨ 3 , 6 ⟩ r

Q7:

Write the vector equation of the straight line that passes through the point βŸ¨βˆ’6,βˆ’9⟩ with direction vector ⟨9,βˆ’2⟩.

  • A r K = ⟨ 9 , βˆ’ 2 ⟩ + ⟨ βˆ’ 6 , βˆ’ 9 ⟩
  • B r K = ⟨ βˆ’ 6 , βˆ’ 9 ⟩ + ⟨ 9 , βˆ’ 2 ⟩
  • C K r = ⟨ 9 , βˆ’ 2 ⟩ + ⟨ βˆ’ 6 , βˆ’ 9 ⟩
  • D K r = ⟨ βˆ’ 6 , βˆ’ 9 ⟩ + ⟨ 9 , βˆ’ 2 ⟩

Q8:

Find the vector equation of the straight line that is parallel to the π‘₯-axis and passing through the point (βˆ’5,2).

  • A r K = ⟨ 2 , βˆ’ 5 ⟩ + ⟨ 1 , 0 ⟩
  • B r K = ⟨ βˆ’ 5 , 2 ⟩ + ⟨ 1 , 0 ⟩
  • C r K = ⟨ 2 , βˆ’ 5 ⟩ + ⟨ 0 , 1 ⟩
  • D r K = ⟨ βˆ’ 5 , 2 ⟩ + ⟨ 0 , 1 ⟩

Q9:

Consider the line through the point (0,4) and perpendicular to vector r=⟨0,4⟩. Which of the following is a vector equation of this line?

  • A 𝐾 = ⟨ 0 , 4 ⟩ + ⟨ 4 , 0 ⟩ r
  • B r = ⟨ 0 , 4 ⟩ + 𝐾 ⟨ 4 , 0 ⟩
  • C r = ⟨ 0 , 4 ⟩ + 𝐾 ⟨ 0 , 4 ⟩
  • D r = ⟨ 4 , 0 ⟩ + 𝐾 ⟨ 0 , 4 ⟩
  • E 𝐾 = ⟨ 0 , 4 ⟩ + ⟨ 0 , 4 ⟩ r

Q10:

Given that (9,1) and (βˆ’8,π‘š) are the direction vectors of two perpendicular straight lines, determine the value of π‘š.

  • A72
  • B βˆ’ 7 2
  • C βˆ’ 8 9
  • D 8 9

Q11:

Suppose that a line has direction vector u=⟨21,4⟩. What, to the nearest second, is the measure of the positive angle that this line makes with the positive π‘₯-axis?

  • A 1 6 9 1 2 β€² 5 7 β€² β€² ∘
  • B 7 9 1 2 β€² 5 7 β€² β€² ∘
  • C 1 0 0 4 7 β€² 3 β€² β€² ∘
  • D 1 0 4 7 β€² 3 β€² β€² ∘

Q12:

If the straight line that passes through the two points (π‘˜,6) and (βˆ’2,βˆ’2) is perpendicular to the one that makes an angle of 14759β€²40β€²β€²βˆ˜ with the positive direction of the π‘₯-axis, find the value of π‘˜ to the nearest integer.

  • A βˆ’ 8
  • B βˆ’ 7
  • C3
  • D βˆ’ 1 3

Q13:

Which of the following is a direction vector of the straight line π‘Žπ‘₯+𝑏𝑦+𝑐=0?

  • A ( π‘Ž , 𝑏 )
  • B ( 𝑏 , βˆ’ π‘Ž )
  • C ( βˆ’ π‘Ž , βˆ’ 𝑏 )
  • D ( π‘Ž , βˆ’ 𝑏 )
  • E ( 𝑏 , π‘Ž )

Q14:

Which of the following is a directional vector for a line perpendicular to the π‘₯-axis?

  • A j = ⟨ 0 , 1 ⟩
  • B i = ⟨ 1 , 0 ⟩

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